1. Field of the Invention
This invention relates to a fuzzy reasoning device. More specifically, this invention relates to an apparatus utilizing membership functions, the roots of fuzzy logic that were developed by Lofti Zadeh circa 1965, to evaluate an object or a process. A membership function represents a set with indistinct boundaries, hence the term "fuzzy". Fuzzy sets differ from crisp, Boolean type logic in that, as opposed to the latter, a fuzzy set allows for shades of grey. Accordingly, each element of a membership function is given a grade which is a percentage of how definitely the element fits into the fuzzy set.
For example, a membership function representing an average workweek for a businessman might produce a grade of 100%, or 1, for a variable value of 40 hours, a grade of 0.6 for a variable value of either 35 or 44 hours, and a grade of 0.1 for a variable value of either 53 or 20 hours. In this fuzzy set, a businessman who worked more than 53 or less than 20 hours a week would have a 0% membership in the membership function and, on the basis of the fuzzy rule defining the membership function, would be said not to have an average workweek.
As can be seen, fuzzy logic represents human logic much more closely than traditional Boolean logic, which, in the above example, would determined that someone who worked 20 hours a week had an average workweek while someone who worked 19 hours a week did not. Furthermore, just as a human makes numerous, unconscious fuzzy type calculations for each decision, a fuzzy reasoning machine can apply many differing fuzzy rules to arrive at one specific determination. The avove example only had one fuzzy rule comprised of one term, an average workweek. More complex problems require application of a plurality of fuzzy rules, each comprised of a plurality of fuzzy terms. A fuzzy rule is expressed in the following form: EQU If (x1=A and x2=B . . . ) then (y=z)
The "If" clause is called the antecedent and the "then" clause is called the consequent. Furthermore, each "x" represents an input variable and "y" represents an output variable. Each capital letter represents a fuzzy label which can be represented by a membership function. Finally, each "=" pairing, for example (x1=A), represents a fuzzy term which can be applied to a specific part of a graph of a membership function.
FIG. 8 shows how membership functions for each variable can be logically combined to produce an output membership function for a fuzzy rule and, moreover, how to combine fuzzy rule output membership functions to achieve one defuzzified result. As can be seen, FIGS. 8(A) and 8(B) represent membership functions wherein x1 and x2, the horizontal axis, indicate variables and A and B are membership functions representing fuzzy labels. Furthermore, the vertical axis value at the point of intersection of the fuzzy label membership function and the variable values, x1' and x2', represents a grade of membership. Thus, in FIG. 8(A), 0.5 represents the first term's grade in the antecedent of the first rule. In FIG. 8(B), 0.3 represents the second term's grade in the antecedent of the first rule.
FIG. 8(C) illustrates the manner in which the antecedent terms are combined to form the consequent. Since the antecedent terms are connected by an "and", their combined graph must be an intersection of the two. This process is referred to as a minimum function corresponding to a mini/max rule. When combining "or"s as in combining consequents, a maximum function applies and the result will not be an intersection of the membership functions. Since the mini rule applies in FIG. 8(C), the output membership function is truncated at the minimum membership grade value, 0.3, of the two input functions. The mesa, indicated by "S", is the consequent and represents all the membership grade values of the variables common to both antecedent terms. Furthermore, y' is located at the center of gravity of the shaded mesa "S" and indicates the final inference determined by the fuzzy rule. In this case, there are only two terms in the antecedent. However, when more terms comprise an antecedent, the combination process is the same.
When, as is usually the case, more than one rule applies to a problem, the above-described process is used to determine the result for each fuzzy rule. However, as shown in FIG. 8(D), each result is not minimized as in the case of combining antecedent terms connected by "and"s but maximized because rules are theoretically connected by "or"s; they are different rules concerning the same phenomenon. Thus, in FIG. 8(D), two mesa portions from two rules are combined according to the max rule and the combined center of gravity is obtained at point y", and the final result of the problem is obtained.
2. Related Art
Conventionally, there are sensory inspection devices for evaluating an object on behalf of a human. One of such conventional devices is unpublished Japanese Publication #61-23966. In this device, sounds are recorded by a microphone and compared with a pre-stored sound wavelength or frequency level. Using this device, an operator can create a sound and gain previously unattainable information about an object. For example, an operator could strike the side of a pumpkin and the apparatus would compare the sound with stored sounds of pumpkins being struck and issue a determination regarding the quality of the fruit.
However, this device has several drawbacks. First, the basis of comparison can only be made if a sound exactly apparatus, the comparison can only be made if a sound exactly corresponds to a prerecorded sound. Similarly, a standard of evaluation may vary from time to time. For instance, one person may want a pumpkin to make a jack-o-lantern while another may desire to make a pumpkin pie. In sum, the importance of a plurality of evaluation values are not constant. Finally, not only is the device limited by relying solely on stored standard patterns, but also such patterns are difficult to change as the expert himself must alter the frequency levels.